arXiv subjects

Bernhard Schölkopf

Publications and source records attributed to Bernhard Schölkopf.

At least 433 records · Page 24Linked to original sources

arXiv2018

Structural causal models for macro-variables in time-series

We consider a bivariate time series $(X_t,Y_t)$ that is given by a simple linear autoregressive model. Assuming that the equations describing each variable as a linear combination of past values are considered structural equations, there is a clear meaning of how intervening on one particular $X_t$ influences $Y_{t'}$ at later times $t'>t$. In the present work, we describe conditions under which one can define a causal model between variables that are coarse-grained in time, thus admitting statements like `setting $X$ to $x$ changes $Y$ in a certain way' without referring to specific time instances. We show that particularly simple statements follow in the frequency domain, thus providing meaning to interventions on frequencies.

math.ST↗

arXiv2018

Experimental and causal view on information integration in autonomous agents

The amount of digitally available but heterogeneous information about the world is remarkable, and new technologies such as self-driving cars, smart homes, or the internet of things may further increase it. In this paper we present preliminary ideas about certain aspects of the problem of how such heterogeneous information can be harnessed by autonomous agents. After discussing potentials and limitations of some existing approaches, we investigate how \emph{experiments} can help to obtain a better understanding of the problem. Specifically, we present a simple agent that integrates video data from a different agent, and implement and evaluate a version of it on the novel experimentation platform \emph{Malmo}. The focus of a second investigation is on how information about the hardware of different agents, the agents' sensory data, and \emph{causal} information can be utilized for knowledge transfer between agents and subsequently more data-efficient decision making. Finally, we discuss potential future steps w.r.t.\ theory and experimentation, and formulate open questions.

cs.AI↗

arXiv2018

Adversarial Extreme Multi-label Classification

The goal in extreme multi-label classification is to learn a classifier which can assign a small subset of relevant labels to an instance from an extremely large set of target labels. Datasets in extreme classification exhibit a long tail of labels which have small number of positive training instances. In this work, we pose the learning task in extreme classification with large number of tail-labels as learning in the presence of adversarial perturbations. This view motivates a robust optimization framework and equivalence to a corresponding regularized objective. Under the proposed robustness framework, we demonstrate efficacy of Hamming loss for tail-label detection in extreme classification. The equivalent regularized objective, in combination with proximal gradient based optimization, performs better than state-of-the-art methods on propensity scored versions of precision@k and nDCG@k(upto 20% relative improvement over PFastreXML - a leading tree-based approach and 60% relative improvement over SLEEC - a leading label-embedding approach). Furthermore, we also highlight the sub-optimality of a sparse solver in a widely used package for large-scale linear classification, which is interesting in its own right. We also investigate the spectral properties of label graphs for providing novel insights towards understanding the conditions governing the performance of Hamming loss based one-vs-rest scheme vis-à-vis label embedding methods.

stat.ML↗

arXiv2018

Avoiding Discrimination through Causal Reasoning

Recent work on fairness in machine learning has focused on various statistical discrimination criteria and how they trade off. Most of these criteria are observational: They depend only on the joint distribution of predictor, protected attribute, features, and outcome. While convenient to work with, observational criteria have severe inherent limitations that prevent them from resolving matters of fairness conclusively. Going beyond observational criteria, we frame the problem of discrimination based on protected attributes in the language of causal reasoning. This viewpoint shifts attention from "What is the right fairness criterion?" to "What do we want to assume about the causal data generating process?" Through the lens of causality, we make several contributions. First, we crisply articulate why and when observational criteria fail, thus formalizing what was before a matter of opinion. Second, our approach exposes previously ignored subtleties and why they are fundamental to the problem. Finally, we put forward natural causal non-discrimination criteria and develop algorithms that satisfy them.

stat.ML↗

arXiv2017

Discriminative k-shot learning using probabilistic models

This paper introduces a probabilistic framework for k-shot image classification. The goal is to generalise from an initial large-scale classification task to a separate task comprising new classes and small numbers of examples. The new approach not only leverages the feature-based representation learned by a neural network from the initial task (representational transfer), but also information about the classes (concept transfer). The concept information is encapsulated in a probabilistic model for the final layer weights of the neural network which acts as a prior for probabilistic k-shot learning. We show that even a simple probabilistic model achieves state-of-the-art on a standard k-shot learning dataset by a large margin. Moreover, it is able to accurately model uncertainty, leading to well calibrated classifiers, and is easily extensible and flexible, unlike many recent approaches to k-shot learning.

stat.ML↗

arXiv2017

Discovering Causal Signals in Images

This paper establishes the existence of observable footprints that reveal the "causal dispositions" of the object categories appearing in collections of images. We achieve this goal in two steps. First, we take a learning approach to observational causal discovery, and build a classifier that achieves state-of-the-art performance on finding the causal direction between pairs of random variables, given samples from their joint distribution. Second, we use our causal direction classifier to effectively distinguish between features of objects and features of their contexts in collections of static images. Our experiments demonstrate the existence of a relation between the direction of causality and the difference between objects and their contexts, and by the same token, the existence of observable signals that reveal the causal dispositions of objects.

stat.ML↗

arXiv2017

A pixel-level model for event discovery in time-domain imaging

Difference imaging or image subtraction is a method that measures differential photometry by matching the pointing and point-spread function (PSF) between image frames. It is used for the detection of time-variable phenomena. Here we present a new category of method---CPM Difference Imaging, in which differences are not measured between matched images but instead between image frames and a data-driven predictive model that has been designed only to predict the pointing, PSF, and detector effects but not astronomical variability. In CPM Difference Imaging each pixel is modelled by the Causal Pixel Model (CPM) originally built for modeling Kepler data, in which pixel values are predicted by a linear combination of other pixels at the same epoch but far enough away such that these pixels are causally disconnected, astrophysically. It does not require that the user have any explicit model or description of the pointing or point-spread function of any of the images. Its principal drawback is that---in its current form---it requires an imaging campaign with many epochs and fairly stable telescope pointing. The method is applied to simulated data and also the K2 Campaign 9 microlensing data. We show that CPM Difference Imaging can detect variable objects and produce precise differentiate photometry in a crowded field. CPM Difference Imaging is capable of producing image differences at nearly photon-noise precision.

astro-ph.IM↗

arXiv2017

Learning Blind Motion Deblurring

As handheld video cameras are now commonplace and available in every smartphone, images and videos can be recorded almost everywhere at anytime. However, taking a quick shot frequently yields a blurry result due to unwanted camera shake during recording or moving objects in the scene. Removing these artifacts from the blurry recordings is a highly ill-posed problem as neither the sharp image nor the motion blur kernel is known. Propagating information between multiple consecutive blurry observations can help restore the desired sharp image or video. Solutions for blind deconvolution based on neural networks rely on a massive amount of ground-truth data which is hard to acquire. In this work, we propose an efficient approach to produce a significant amount of realistic training data and introduce a novel recurrent network architecture to deblur frames taking temporal information into account, which can efficiently handle arbitrary spatial and temporal input sizes. We demonstrate the versatility of our approach in a comprehensive comparison on a number of challening real-world examples.

cs.CV↗

arXiv2017

EnhanceNet: Single Image Super-Resolution Through Automated Texture Synthesis

Single image super-resolution is the task of inferring a high-resolution image from a single low-resolution input. Traditionally, the performance of algorithms for this task is measured using pixel-wise reconstruction measures such as peak signal-to-noise ratio (PSNR) which have been shown to correlate poorly with the human perception of image quality. As a result, algorithms minimizing these metrics tend to produce over-smoothed images that lack high-frequency textures and do not look natural despite yielding high PSNR values. We propose a novel application of automated texture synthesis in combination with a perceptual loss focusing on creating realistic textures rather than optimizing for a pixel-accurate reproduction of ground truth images during training. By using feed-forward fully convolutional neural networks in an adversarial training setting, we achieve a significant boost in image quality at high magnification ratios. Extensive experiments on a number of datasets show the effectiveness of our approach, yielding state-of-the-art results in both quantitative and qualitative benchmarks.

cs.CV↗

arXiv2017

Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.

stat.ML↗

arXiv2017

Interpolated Policy Gradient: Merging On-Policy and Off-Policy Gradient Estimation for Deep Reinforcement Learning

Off-policy model-free deep reinforcement learning methods using previously collected data can improve sample efficiency over on-policy policy gradient techniques. On the other hand, on-policy algorithms are often more stable and easier to use. This paper examines, both theoretically and empirically, approaches to merging on- and off-policy updates for deep reinforcement learning. Theoretical results show that off-policy updates with a value function estimator can be interpolated with on-policy policy gradient updates whilst still satisfying performance bounds. Our analysis uses control variate methods to produce a family of policy gradient algorithms, with several recently proposed algorithms being special cases of this family. We then provide an empirical comparison of these techniques with the remaining algorithmic details fixed, and show how different mixing of off-policy gradient estimates with on-policy samples contribute to improvements in empirical performance. The final algorithm provides a generalization and unification of existing deep policy gradient techniques, has theoretical guarantees on the bias introduced by off-policy updates, and improves on the state-of-the-art model-free deep RL methods on a number of OpenAI Gym continuous control benchmarks.

cs.LG↗

arXiv2017

Local Group Invariant Representations via Orbit Embeddings

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distribution over the group which in turn induces distributions in the input feature space. We learn a decision function over these distributions by appealing to the powerful framework of kernel methods and generate local invariant random feature maps via kernel approximations. We show uniform convergence bounds for kernel approximation and provide excess risk bounds for learning with these features. We evaluate our method on three real datasets, including Rotated MNIST and CIFAR-10, and observe that it outperforms competing kernel based approaches. The proposed method also outperforms deep CNN on Rotated-MNIST and performs comparably to the recently proposed group-equivariant CNN.

cs.LG↗

arXiv2017

AdaGAN: Boosting Generative Models

Generative Adversarial Networks (GAN) (Goodfellow et al., 2014) are an effective method for training generative models of complex data such as natural images. However, they are notoriously hard to train and can suffer from the problem of missing modes where the model is not able to produce examples in certain regions of the space. We propose an iterative procedure, called AdaGAN, where at every step we add a new component into a mixture model by running a GAN algorithm on a reweighted sample. This is inspired by boosting algorithms, where many potentially weak individual predictors are greedily aggregated to form a strong composite predictor. We prove that such an incremental procedure leads to convergence to the true distribution in a finite number of steps if each step is optimal, and convergence at an exponential rate otherwise. We also illustrate experimentally that this procedure addresses the problem of missing modes.

stat.ML↗

arXiv2017

Annealed Generative Adversarial Networks

We introduce a novel framework for adversarial training where the target distribution is annealed between the uniform distribution and the data distribution. We posited a conjecture that learning under continuous annealing in the nonparametric regime is stable irrespective of the divergence measures in the objective function and proposed an algorithm, dubbed ß-GAN, in corollary. In this framework, the fact that the initial support of the generative network is the whole ambient space combined with annealing are key to balancing the minimax game. In our experiments on synthetic data, MNIST, and CelebA, ß-GAN with a fixed annealing schedule was stable and did not suffer from mode collapse.

stat.ML↗

arXiv2017

Personalized Brain-Computer Interface Models for Motor Rehabilitation

We propose to fuse two currently separate research lines on novel therapies for stroke rehabilitation: brain-computer interface (BCI) training and transcranial electrical stimulation (TES). Specifically, we show that BCI technology can be used to learn personalized decoding models that relate the global configuration of brain rhythms in individual subjects (as measured by EEG) to their motor performance during 3D reaching movements. We demonstrate that our models capture substantial across-subject heterogeneity, and argue that this heterogeneity is a likely cause of limited effect sizes observed in TES for enhancing motor performance. We conclude by discussing how our personalized models can be used to derive optimal TES parameters, e.g., stimulation site and frequency, for individual patients.

cs.HC↗

arXiv2017

Group invariance principles for causal generative models

The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches. In our setting, the cause-mechanism relationship is assessed by comparing it against a null hypothesis through the application of random generic group transformations. We show that the group theoretic view provides a very general tool to study the structure of data generating mechanisms with direct applications to machine learning.

stat.ML↗

arXiv2017

Online Video Deblurring via Dynamic Temporal Blending Network

State-of-the-art video deblurring methods are capable of removing non-uniform blur caused by unwanted camera shake and/or object motion in dynamic scenes. However, most existing methods are based on batch processing and thus need access to all recorded frames, rendering them computationally demanding and time consuming and thus limiting their practical use. In contrast, we propose an online (sequential) video deblurring method based on a spatio-temporal recurrent network that allows for real-time performance. In particular, we introduce a novel architecture which extends the receptive field while keeping the overall size of the network small to enable fast execution. In doing so, our network is able to remove even large blur caused by strong camera shake and/or fast moving objects. Furthermore, we propose a novel network layer that enforces temporal consistency between consecutive frames by dynamic temporal blending which compares and adaptively (at test time) shares features obtained at different time steps. We show the superiority of the proposed method in an extensive experimental evaluation.

cs.CV↗

arXiv2017

A note on the expected minimum error probability in equientropic channels

While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely many bits. In this note, we characterise the quality of a code (i. e. a given encoding routine) by an upper bound on the expected minimum error probability that can be achieved when using this code. We show that for equientropic channels this upper bound is minimal for codes with maximal marginal entropy. As an instructive example we show for the additive white Gaussian noise (AWGN) channel that random coding---also a capacity achieving code---indeed maximises the marginal entropy in the limit of infinite messages.

q-bio.NC↗